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Finding the Third Proportional to 138.82 and 209.30

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Solution

The third proportional to 138.82 and 209.30 is: 315.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    138.82 : 209.30 = 209.30 : x
  2. Step 2: Convert to fraction form
    138.82/209.30 = 209.30/x
  3. Step 3: Cross multiply
    138.82x = 209.30 × 209.30
  4. Step 4: Simplify right side
    138.82x = 43,807.63
  5. Step 5: Solve for x
    x = 43,807.63/138.82
  6. Step 6: Final answer
    x = 315.56

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.